Influence of subgrid scales on resolvable turbulence and mixing in Rayleigh–Taylor flow

<jats:p>The energy transfer process and the interaction of different scales in a flow induced by the variable-density Rayleigh–Taylor instability in miscible fluids is investigated using a three-dimensional direct numerical simulation database with a spatial resolution of Nx×Ny×Nz=512×512×2040. The method used to study the transfer of energy between the supergrid and subgrid scales in the homogeneous planes, determined by partitioning the modes into resolved and unresolved scales defined by a two-dimensional cutoff wave number kc in Fourier space, is applied to the kinetic energy evolution equation. The treatment of the flow inhomogeneity in the direction z parallel to the acceleration is analogous to that used in the analysis of incompressible wall-bounded flows, including channel flow and Rayleigh–Bénard convection [J. A. Domaradzki et al., Phys. Fluids 6, 1583 (1994); J. A. Domaradzki and W. Liu, ibid. 7, 2025 (1995)]. Using a sharp Fourier cutoff filter, the kinetic energy transfer is decomposed into (1) the resolved part; (2) a part corresponding to the interaction between resolved and unresolved scales; and (3) a part corresponding to the interaction between unresolved scales. The sum of these last two contributions is the subgrid-scale kinetic energy transfer, which is studied in the present work. These z-dependent spectra are computed for three different cutoff wave numbers to investigate the dependence of the transfer process on the scales contributing to the subgrid interactions. The kinetic energy transfer is further decomposed into its positive and negative components corresponding to the forward and backward cascades of energy, respectively, that arise from the nonlinear modal interactions. The decomposition into resolved and unresolved scales is used to define an effective eddy viscosity and backscatter viscosity. The principal conclusions of the analysis are (1) the transfer spectra and eddy viscosities exhibit a strong dependence on the wave number cutoff; (2) the contributions from the interaction between resolved and unresolved scales dominate the contribution to the total subgrid eddy viscosities and are responsible for the cusp at large k/kc; (3) the contributions from the interaction between unresolved scales dominate the contribution to the total subgrid eddy viscosities at small k/kc and are responsible for the small, negative contribution (associated with an inverse energy transfer), and (4) backscatter is strongest in the regions near the boundaries of the mixing layer. The physical implications of these results for subgrid-scale modeling in a large-eddy simulation of Rayleigh–Taylor instability-induced turbulence are discussed.</jats:p>